H∞ sliding mode control of discrete switched systems with time-varying delays

The finite-time boundedness issue for a class of discrete switched systems with time-varying delays is investigated via sliding mode control (SMC) approach. By employing the Lyapunov functional and average dwell time method, new sufficient conditions are derived to guarantee the finite-time boundedness of the dynamic system in the novel sliding surface. By solving an optimization problem, the sliding mode controller is synthesized such that the discrete reaching condition is satisfied and the chattering is reduced. A simulation example tests the feasibility of the provided SMC scheme.     

Finite-time stability for discrete-time system with time-varying delay and nonlinear perturbations

In this paper, the problem of finite-time stability for discrete-time system with time-varying delay and nonlinear perturbations is investigated. By constructing a novel Lyapunov–Krasovskii functional and employing a new summation inequality named discrete Wirtinger-based inequality, reciprocally convex approach and zero equality, the improved finite-time stability criteria are derived to guarantee that the state of the system with time-varying delay does not exceed a given threshold when fixed time interval. Furthermore, the obtained conditions are formulated in forms of linear matrix inequalities which can be solved by using some standard numerical packages. Finally, three numerical examples are given to show the effectiveness and less conservatism of the proposed method.     

Sampled-data-based vibration control for structural systems with finite-time state constraint and sensor outage

The problem of sampled-data-based vibration control for structural systems with finite-time state constraint and sensor outage is investigated in this paper. The objective of designing controllers is to guarantee the stability and anti-disturbance performance of the closed-loop systems while some sensor outages happen. Firstly, based on matrix transformation, the state-space model of structural systems with sensor outages and uncertainties appearing in the mass, damping and stiffness matrices is established. Secondly, by considering most of those earthquakes or strong winds happen in a very short time, and it is often the peak values make the structures damaged, the finite-time stability analysis method is introduced to constrain the state responses in a given time interval, and the H-infinity stability is adopted in the controller design to make sure that the closed-loop system has a prescribed level of disturbance attenuation performance during the whole control process. Furthermore, all stabilization conditions are expressed in the forms of linear matrix inequalities (LMIs), whose feasibility can be easily checked by using the LMI Toolbox. Finally, numerical examples are given to demonstrate the effectiveness of the proposed theorems.     

Finite-time decentralized adaptive neural constrained control for interconnected nonlinear time-delay systems with dynamics couplings among subsystems

The problem of finite-time decentralized neural adaptive constrained control is studied for large-scale nonlinear time-delay systems in the non-affine form. The main features of the considered system are that 1) unknown unmatched time-delay interactions are considered, 2) the couplings among the nested subsystems are involved in uncertain nonlinear systems, 3) based on finite-time stability approach, asymmetric saturation actuators and output constraints are studied in large-scale systems. First, the smooth asymmetric saturation nonlinearity and barrier Lyapunov functions are used to achieve the input and output constraints. Second, the appropriately designed Lyapunov-Krasovskii functional and the property of hyperbolic tangent functions are used to deal with the unknown unmatched time-delay interactions, and the neural networks are employed to approximate the unknown nonlinearities. Note that, due to unknown time-delay interactions and the couplings among subsystems, the controller design is more meaningful and challenging. At last, based on finite-time stability theory and Lyapunov stability theory, a decentralized adaptive controller is proposed, which decreases the number of learning parameters. It is shown that the designed controller can ensure that all closed-loop signals are bounded and the tracking error converges to a small neighborhood of the origin. The simulation studies are presented to show the effectiveness of the proposed method.     

Finite-time master–slave synchronization and parameter identification for uncertain Lurie systems

This paper investigates the finite-time master–slave synchronization and parameter identification problem for uncertain Lurie systems based on the finite-time stability theory and the adaptive control method. The finite-time master–slave synchronization means that the state of a slave system follows with that of a master system in finite time, which is more reasonable than the asymptotical synchronization in applications. The uncertainties include the unknown parameters and noise disturbances. An adaptive controller and update laws which ensures the synchronization and parameter identification to be realized in finite time are constructed. Finally, two numerical examples are given to show the effectiveness of the proposed method.     

Finite-time stabilization for a class of stochastic nonlinear systems via output feedback

This paper investigates the problem of global finite-time stabilization in probability for a class of stochastic nonlinear systems. The drift and diffusion terms satisfy lower-triangular or upper-triangular homogeneous growth conditions. By adding one power integrator technique, an output feedback controller is first designed for the nominal system without perturbing nonlinearities. Based on homogeneous domination approach and stochastic finite-time stability theorem, it is proved that the solution of the closed-loop system will converge to the origin in finite time and stay at the origin thereafter with probability one. Two simulation examples are presented to illustrate the effectiveness of the proposed design procedure.     

Attitude output feedback control for rigid spacecraft with finite-time convergence

The main problem addressed is the quaternion-based attitude stabilization control of rigid spacecraft without angular velocity measurements in the presence of external disturbances and reaction wheel friction as well. As a stepping stone, an angular velocity observer is proposed for the attitude control of a rigid body in the absence of angular velocity measurements. The observer design ensures finite-time convergence of angular velocity state estimation errors irrespective of the control torque or the initial attitude state of the spacecraft. Then, a novel finite-time control law is employed as the controller in which the estimate of the angular velocity is used directly. It is then shown that the observer and the controlled system form a cascaded structure, which allows the application of the finite-time stability theory of cascaded systems to prove the finite-time stability of the closed-loop system. A rigorous analysis of the proposed formulation is provided and numerical simulation studies are presented to help illustrate the effectiveness of the angular-velocity observer for rigid spacecraft attitude control.     

Finite-time stabilization for a class of nonholonomic feedforward systems subject to inputs saturation

This paper studies the problem of finite-time stabilization by state feedback for a class of uncertain nonholonomic systems in feedforward-like form subject to inputs saturation. Under the weaker homogeneous condition on systems growth, a saturated finite-time control scheme is developed by exploiting the adding a power integrator method, the homogeneous domination approach and the nested saturation technique. Together with a novel switching control strategy, the designed saturated controller guarantees that the states of closed-loop system are regulated to zero in a finite time without violation of the constraint. As an application of the proposed theoretical results, the problem of saturated finite-time control for vertical wheel on rotating table is solved. Simulation results are given to demonstrate the effectiveness of the proposed method.     

Relative position finite-time coordinated tracking control of spacecraft formation without velocity measurements

This paper investigates finite-time relative position coordinated tracking problem by output feedback for spacecraft formation flying without velocity measurement. By employing homogeneous system theory, a finite-time relative position coordinated tracking controller by state feedback is firstly developed, where the desired time-varying trajectory given in advance can be tracked by the formation. Then, to address the problem of lack of velocity measurements, a finite-time output feedback controller is proposed by involving a novel filter to recover unknown velocity information in a finite time. Rigorous proof shows that the proposed control law ensures global stability and guarantees the position of spacecraft formation to track a time-varying reference in finite time. Finally, simulation results are presented to illustrate the performance of the proposed controller.     

Finite-time state-dependent Riccati equation for time-varying nonaffine systems: Rigid and flexible joint manipulator control

This article investigates finite-time optimal and suboptimal controls for time-varying systems with state and control nonlinearities. The state-dependent Riccati equation (SDRE) controller was the main framework. A finite-time constraint imposed on the equation changes it to a differential equation, known as the state-dependent differential Riccati equation (SDDRE) and this equation was applied to the problem reported in this study that provides general formulation and stability analysis. The following four solution methods were developed for solving the SDDRE; backward integration, state transition matrix (STM) and the Lyapunov based method. In the Lyapunov approach, both positive and negative definite solutions to related SDRE were used to provide suboptimal gain for the SDDRE. Finite-time suboptimal control is applied for robotic manipulator, as finite-time constraint strongly decreases state error and operation time. General state-dependent coefficient (SDC) parameterizations for rigid and flexible joint arms (prismatic or revolute joints) are introduced. By including nonlinear control inputs in the formulation, the actuator׳s limits can be inserted directly to the state-space equation of a manipulator. A finite-time SDRE was implemented on a 6R manipulator both in theory and experimentally. And a reduced 3R arm was modeled and tested as a flexible joint robot (FJR). Evaluations of load carrying capacity and operation time were investigated to assess the capability of this approach, both of which showed significant improvement.     

Finite-time Extended State Observer based fault tolerant output feedback control for attitude stabilization

This work addresses the challenging problem of finite-time fault tolerant attitude stabilization control for the rigid spacecraft attitude control system without the angular velocity measurements, in the presence of external disturbances and actuator failures. Consider the severe circumstances with above failures and uncertainties, a novel continuous finite-time Extended State Observer is first established to observe the attitude angular velocity and the synthetic failure simultaneously. Unlike the existing observers, the finite-time methodology and Extended State Observer are utilized, to achieve the finite-time uniformly ultimately bounded stability of the attitude angular velocity and extended state observation errors. Furthermore, a novel continuous finite-time attitude controller is developed by using the nonsingular terminal sliding mode control and super-twisting method. The main feature of this work stems from our use of multiply advanced techniques or methodologies that enables the finite-time stability of the closed-loop attitude control system and the designed control scheme is continuous with the property of chattering restraining. Finally, numerical simulation results are presented to illustrate the effectiveness and fine performances of the finite-time observer and controller for the attitude control system.     

A new robust control for minirotorcraft unmanned aerial vehicles

This paper presents a new robust control based on finite-time Lyapunov stability controller and proved with backstepping method for the position and the attitude of a small rotorcraft unmanned aerial vehicle subjected to bounded uncertainties and disturbances. The dynamical motion equations are obtained by the Newton–Euler formalism. The proposed controller combines the advantage of the backstepping approach with finite-time convergence techniques to generate a control laws to guarantee the faster convergence of the state variables to their desired values in short time and compensate for the bounded disturbances. A formal proof of the closed-loop stability and finite-time convergence of tracking errors is derived using the Lyapunov function technique. Simulation results are presented to corroborate the effectiveness and the robustness of the proposed control method.     

Impulsive stabilization of fractional differential systems

This paper investigates the impulsive stabilization problem of fractional differential systems (FDSs in short). Both the global exponential stability and ultimate boundedness criteria are established using Lyapunov functions, algebraic inequality techniques and boundedness of Mittag-Leffler functions. It is shown that unstable and unbounded FDSs can be stable and bounded respectively under impulsive control. Examples and simulations are also provided to demonstrate the effectiveness of the derived theoretical results.     

Global finite-time adaptive control for uncalibrated robot manipulator based on visual servoing

The paper addresses the finite-time convergence problem of a uncalibrated camera-robot system with uncertainties. These uncertainties include camera extrinsic and intrinsic parameters, robot dynamics and feature depth parameters, which are all considered as time-varying uncertainties. In order to achieve a better dynamic stability performance of the camera-robot system, a novel FTS adaptive controller is presented to cope with rapid convergence problem. Meanwhile, FTS adaptive laws are proposed to handle these uncertainties which exist both in robot and in camera model. The finite-time stability analysis is discussed in accordance with homogeneous theory and Lyapunov function formalism. The control method we proposed extends the asymptotic stability results of visual servoing control to a finite-time stability. Simulation has been conducted to demonstrate the performance of the trajectory tracking errors convergence under control of the proposed method.     

Adaptive sliding mode control for finite-time stability of quad-rotor UAVs with parametric uncertainties

Adaptive control methods are developed for stability and tracking control of flight systems in the presence of parametric uncertainties. This paper offers a design technique of adaptive sliding mode control (ASMC) for finite-time stabilization of unmanned aerial vehicle (UAV) systems with parametric uncertainties. Applying the Lyapunov stability concept and finite-time convergence idea, the recommended control method guarantees that the states of the quad-rotor UAV are converged to the origin with a finite-time convergence rate. Furthermore, an adaptive-tuning scheme is advised to guesstimate the unknown parameters of the quad-rotor UAV at any moment. Finally, simulation results are presented to exhibit the helpfulness of the offered technique compared to the previous methods.     

Finite-time extended dissipative control for fuzzy systems with nonlinear perturbations via sampled-data and quantized controller

This paper investigates the problem of finite-time extended dissipative control for T–S fuzzy time-varying delay systems with nonlinear perturbations via sampled-data and quantized controller. The definition of finite-time bounded mixed extended dissipative of fuzzy systems is first proposed. Based on the constructed Lyapunov–Krasovskii functional(LKF) and Peng–Parks integral inequality, some sufficient conditions are obtained in the form of linear matrix inequalities(LMIs), which are less conservative than other papers. By combining the input delay approach and dynamic quantizer, the sampled-data and quantized controller is designed to guarantee that the T–S fuzzy system is finite-time bounded mixed extended dissipative. Finally, some numerical examples and practical examples are presented to verify the feasibility and effectiveness of the proposed methods.     

Robust finite-time consensus control for multi-agent systems with disturbances and unknown velocities

In this paper, we investigated the finite-time consensus tracking problem for multi-agent systems with external bounded disturbances and input bounded disturbances and unknown velocities. Based on the Lyapunov finite-time theorem, a novel finite-time consensus control is constructed by using the backstepping method. For unknown velocities, the high-gain observer is used to estimate the velocity information. It is proved that the consensus can be achieved in finite time. The consensus shows fast response and strong robustness to various disturbances. Finally, the effectiveness of the results is illustrated by numerical simulations.